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Consider the vector space V = C° with scalar multiplication over the real numbers R and let W- (z1, z2) e V : Zz = z, + 27,}. 1.1 Use the Subspace Test to show that W is a subspace of V. 1.2 Find a basis for W. 1.3 Explain whether W is a subspace over C.

Consider the vector space V = C° with scalar multiplication over the real numbers R and let W- (z1, z2) e V : Zz = z, + 27,}. 1.1 Use the Subspace Test to show that W is a subspace of V. 1.2 Find a basis for W. 1.3 Explain whether W is a subspace over C.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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W Document1 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? % Cut A Find - - 11 - =。三,年 外T Calibri (Body) A A Aa Aal AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL E Copy ae Replace BI U ab A I Normal I No Spaci. Heading 1 Paste abe x, x* A Change . Heading 2 Title Subtitle W Format Painter Styles - Select - Clipboard Font Paragraph Styles Editing • 2. 1:. I' 2: 1 : 3:1 • 4.I 5.1' 6.1'7 I'8: 1 9 ' 10.L· 11: 1 ' 12.'13 · L 14: 1· 15.1A L'17:1 18 LINEAR ALGEBRA PLEASE ANSWwER ALL QUESTIONS Consider the vector space V = C2 with scalar multiplication over the real numbers R and let W {(z1, Z2) E V :Zz = Z1 + 271}. 1.1 Use the Subspace Test to show that W is a subspace of V. 1.2 Find a basis for W. 1.3 Explain whether W is a subspace over C. 06:37 PM 2022-05-10 Page: 1 of 1 Words: 6 E EA E E E 100% - +) 2' I '11• | '10·L •9
Transcribed Image Text:W Document1 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? % Cut A Find - - 11 - =。三,年 外T Calibri (Body) A A Aa Aal AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL E Copy ae Replace BI U ab A I Normal I No Spaci. Heading 1 Paste abe x, x* A Change . Heading 2 Title Subtitle W Format Painter Styles - Select - Clipboard Font Paragraph Styles Editing • 2. 1:. I' 2: 1 : 3:1 • 4.I 5.1' 6.1'7 I'8: 1 9 ' 10.L· 11: 1 ' 12.'13 · L 14: 1· 15.1A L'17:1 18 LINEAR ALGEBRA PLEASE ANSWwER ALL QUESTIONS Consider the vector space V = C2 with scalar multiplication over the real numbers R and let W {(z1, Z2) E V :Zz = Z1 + 271}. 1.1 Use the Subspace Test to show that W is a subspace of V. 1.2 Find a basis for W. 1.3 Explain whether W is a subspace over C. 06:37 PM 2022-05-10 Page: 1 of 1 Words: 6 E EA E E E 100% - +) 2' I '11• | '10·L •9
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